Answer :
Final answer:
The magnitude of vector B is 10.00 units. The correct option is d) because vector B, with a magnitude of 10.00 units, results from the combination of its vertical and horizontal components, determined by the given angle and the magnitude of the SSM vector, respectively. This option represents the correct magnitude of B resulting from vector addition, meeting the conditions outlined in the question. Therefore, d) is the appropriate choice.
Explanation:
The magnitude of vector B can be found using vector addition since both vectors are perpendicular to each other. To find the magnitude of vector B, we use the Pythagorean theorem, where the magnitude of B is the square root of the sum of the squares of the magnitudes of the two vectors. First, we find the horizontal component of B using trigonometry, which is equal to 6.00 units. Then, using the given angle of 60.0° north of east, we find the vertical component of B using trigonometry as well. Combining these two components, we calculate the magnitude of B to be 10.00 units.
In vector addition, the two vectors form a right triangle, where the horizontal component of vector B is adjacent to the angle, and the vertical component is opposite. By applying trigonometric functions, we determine the magnitudes of these components. Then, using the Pythagorean theorem, we find the magnitude of vector B as the hypotenuse of the triangle formed by the two components. Thus, the magnitude of B is 10.00 units.
The angle provided, 60.0° north of east, is crucial in determining the vertical component of vector B. It helps us find the correct direction of B in relation to the east direction. Therefore, incorporating this angle into our calculations ensures an accurate determination of the magnitude of vector B. Thus, we can confidently conclude that the magnitude of vector B is 10.00 units, as calculated.(option d)
